In this section, we use the parameters that satisfy the ATS model in Eqs. (REF ), i.e., \(\gamma _{10}=1\) , \(\gamma _{21} =1.4\) , \(\gamma _{1}^{\phi } =0.4\) , \(\gamma _{2}^{\phi } =0.2\) , \(\Omega _p=1\)  and \(\Omega _{c}=10.8\) , which is also consistent with the parameters in Fig. REF . Then \(\Gamma =0.9\)  and \(\Lambda =0\) , where a non-interference transparency window appears for the un-modulated system. In Fig. REF , we plot the numerical results of \(\mathrm {Im}(\rho _{10})\)  obtained from Eq. (REF ) for the Floquet three-level system. Note that here we only focus on the properties of the CTW and the numerical results is obtained by calculating the dynamic steady states of the Floquet three-level system with time evolution step \(\tau \) . As an objective way to identify the more appropriate model for the CTW in the Floquet three-level system, we also plot the fitting profile for each \(\tau \)  using QI(\(\Omega _{c},\Omega _{p}\) ,\(\Gamma \) ,\(\Lambda \) ) and ATS(\(\Omega _{c},\Omega _{p}\) ,\(\Gamma \) ) models with fitting parameters \(\Omega _{p}\) , \(\Omega _{c}\) , \(\Gamma \)  and \(\Lambda \)  in Eqs. (REF ) and (REF ) as a comparison. For small Floquet period, e.g. \(\tau =0.001\) , ATS and QI fitting
curves merge and both fit well with the simulated absorption. The fitted
value of the interference term \(\Lambda \)  is close to 0, which indicates that
the CTW in rapidly modulated system has the similar properties to the
transparency in it un-modulated counterparts. This could be understood as
the quantum Zeno effect [1]}. For larger Floquet periods,
such as \(\tau =0.05,0.1,0.15\) , we find that the CTW fits better with the QI
model. The fitted interference \(\Lambda <0\) , which indicates constructive
interference in the CTW. This could be understood qualitatively as that the
periodic driving heat the system and effectively change the decay rates.
However, as the modulation frequency \(\omega \)  increases, the heating
speed becomes slower, which is known as Floquet prethermalization [2]}. To conclude, in the ATS's parameter regime, the CTW is
ATS-like but with significant interference adjustable in a wide range of modulation
periods, which differentiates the CTW in the Floquet three-level system from the traditional ATS.
